I use LastPass currently. I believe the benefits of properly unique passwords per site without having to actually remember 100s of them is well known. If not I suggest following Troy Hunt and registering on HaveIBeenPwned and that should be enough to scare the crap out of most.
Mainly chose it because it was centralized which made it easier to sync across all devices without needing another service to store it (i.e. Dropbox) or a bunch of plugins written by other people. Great device integration (iOS + Browser) and it is free. I do download a copy to an offline secure store from time to time though as you never know.